A069048 Numbers k such that (i) k is a concatenation of consecutive natural numbers starting at 1 and (ii) k+1 is prime.

1, 12, 123456, 123456789101112131415161718192021222324252627282930, 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788

Offset

1,2

Comments

Let n be a concatenation of consecutive natural numbers, starting from 1. Is n ever a prime number? [See A007908 for much more about this question. - N. J. A. Sloane, Dec 20 2022]

a(5) has 167 digits. There are no further terms 123...n for n <= 1000 (123...1000 has 2893 digits). - Harvey P. Dale, Dec 20 2022

Links

Table of n, a(n) for n=1..5.

Example

12 is a term since it is the concatenation of 1 and 2, and 12+1 = 13 is prime.
123456 is a concatenation, starting with 1, of consecutive natural numbers and 123456 + 1 = 123457 is prime.
k = 123456789101112131415161718192021222324252627282930 is a term since k+1 = 123456789101112131415161718192021222324252627282931 is prime.

Mathematica

Select[Table[FromDigits[Flatten[IntegerDigits/@Range[n]]], {n, 100}], PrimeQ[#+1]&] (* Harvey P. Dale, Dec 20 2022 *)

Crossrefs

Cf. A007908, A359124, A359125.

Sequence in context: A331093 A369523 A328992 * A284287 A100246 A055323

Adjacent sequences: A069045 A069046 A069047 * A069049 A069050 A069051

Keyword

base,nonn

Author

Joseph L. Pe, Apr 03 2002

Extensions

Corrected by Harvey P. Dale, Dec 20 2022.

Edited by N. J. A. Sloane, Dec 20 2022

Status

approved